TY - JOUR
T1 - 4D Conformal metrics, the eikonal equation and fourth-order ODEs
AU - Marciano-Melchor, Magdalena
AU - Newman, Ezra Ted
AU - Silva-Ortigoza, Gilberto
PY - 2005/12/7
Y1 - 2005/12/7
N2 - In this work we show that on the space of solutions of a certain class of fourth-order ODEs, u″′′ ≤ Λ(s, u, u′, u″, u″′), a four-dimensional conformal metric, gab, can be constructed such that the four-dimensional eikonal equation, g abu,au,b ≤ 0, holds. Furthermore, we remark that this structure is invariant under contact transformations. Our general results are applied to the Minkowski spacetime.
AB - In this work we show that on the space of solutions of a certain class of fourth-order ODEs, u″′′ ≤ Λ(s, u, u′, u″, u″′), a four-dimensional conformal metric, gab, can be constructed such that the four-dimensional eikonal equation, g abu,au,b ≤ 0, holds. Furthermore, we remark that this structure is invariant under contact transformations. Our general results are applied to the Minkowski spacetime.
UR - http://www.scopus.com/inward/record.url?scp=28244493697&partnerID=8YFLogxK
U2 - 10.1088/0264-9381/22/23/010
DO - 10.1088/0264-9381/22/23/010
M3 - Artículo
SN - 0264-9381
VL - 22
SP - 5073
EP - 5088
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
IS - 23
ER -